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arXiv · 2205.12389

Non-degenerate minimal submanifolds as energy concentration sets: a variational approach

Guido De Philippis·Alessandro Pigati
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Abstract

We prove that every non-degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg-Landau functional. The proof is purely variational, and follows the strategy laid out by Jerrard and Sternberg, extending a recent result for geodesics by Colinet-Jerrard-Sternberg. The same proof applies also to the $U(1)$-Yang-Mills-Higgs and to the Allen-Cahn-Hilliard energies.

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Guido De Philippis, Alessandro Pigati. 2022-05-24. Non-degenerate minimal submanifolds as energy concentration sets: a variational approach. https://arxiv.org/abs/2205.12389

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